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Average quantum dynamics of closed systems over stochastic Hamiltonians
Li Yu1,2, Daniel F V James3
1Department of Physics, University of Toronto, 60 St. George Street, Toronto, ON, M5S 1A7, Canada. li.yu.phys@hotmail.com.
Scientific Reports
|August 22, 2025
Summary
We developed a master equation for quantum systems with random influences, revealing decoherence and disentanglement effects. This provides exact dynamics for specific stochastic Hamiltonians, applicable to various quantum systems.
Area of Science:
- Quantum Mechanics
- Statistical Physics
- Quantum Information Theory
Background:
- Closed quantum systems typically evolve unitarily.
- Stochastic processes in quantum systems can induce decoherence.
- Existing models may not capture exact dynamics under stochastic Hamiltonians.
Purpose of the Study:
- To develop a formally exact master equation for closed quantum systems driven by stochastic Hamiltonians.
- To investigate decoherence effects arising from averaging over stochastic processes.
- To identify conditions under which the master equation yields exact dynamics.
Main Methods:
- Derivation of a master equation for the average density matrix.
- Analysis of systems with Hamiltonians proportional to Gaussian random processes.
- Application of the formalism to specific quantum systems (two-level system, two atoms, trapped ion).
Main Results:
- The developed master equation accurately describes the evolution of the average density matrix.
- Decoherence effects are shown to arise from averaging over stochastic processes.
- Exact dynamics are obtained for a class of problems involving Gaussian random processes.
- Phenomena like decoherence-induced disentanglement were observed in studied examples.
Conclusions:
- The master equation provides a powerful tool for studying quantum systems with stochastic driving.
- Stochastic Hamiltonians can lead to significant deviations from purely unitary evolution, including disentanglement.
- The findings have implications for understanding and controlling quantum dynamics in noisy environments.
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